Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 11
sizeConstants = 55
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (minute)"
legend_constants[0] = "V_max1 in component V1 (micromolar_per_minute)"
legend_constants[1] = "GEFt in component V1 (micromolar)"
legend_constants[43] = "V_1 in component V1 (per_minute)"
legend_constants[2] = "Str in component V2 (dimensionless)"
legend_constants[3] = "V_max2 in component V2 (micromolar_per_minute)"
legend_constants[44] = "V_2 in component V2 (per_minute)"
legend_constants[4] = "k_c3 in component V3 (per_minute)"
legend_constants[5] = "PKAt in component V3 (micromolar)"
legend_constants[6] = "GAPt in component V3 (micromolar)"
legend_constants[45] = "V_3 in component V3 (per_minute)"
legend_constants[7] = "V_max4 in component V4 (micromolar_per_minute)"
legend_constants[46] = "V_4 in component V4 (per_minute)"
legend_constants[8] = "k_gef in component V5 (per_minute)"
legend_constants[9] = "RASt in component V5 (micromolar)"
legend_constants[47] = "V_5 in component V5 (per_minute)"
legend_constants[10] = "k_gap in component V6 (per_minute)"
legend_constants[48] = "V_6 in component V6 (per_minute)"
legend_constants[11] = "k_c7 in component V7 (per_minute)"
legend_constants[12] = "PDEt in component V7 (micromolar)"
legend_constants[49] = "V_7 in component V7 (per_minute)"
legend_constants[13] = "V_max8 in component V8 (micromolar_per_minute)"
legend_constants[50] = "V_8 in component V8 (per_minute)"
legend_constants[14] = "a in component VPKAact (per_micromolar_squared_minute)"
legend_constants[15] = "r in component VPKAact (per_minute)"
legend_states[0] = "R2C2 in component holoenzyme_R_C (dimensionless)"
legend_states[1] = "cAMP in component cyclic_AMP (micromolar)"
legend_algebraic[3] = "C in component C_subunit (dimensionless)"
legend_algebraic[0] = "R2cAMP2 in component holoenzyme_R_cAMP (dimensionless)"
legend_algebraic[4] = "V_PKAact in component VPKAact (per_minute)"
legend_constants[16] = "K_1 in component active_GEF (dimensionless)"
legend_constants[17] = "K_2 in component active_GEF (dimensionless)"
legend_states[2] = "GEFa in component active_GEF (dimensionless)"
legend_constants[18] = "K_3 in component active_GAP (dimensionless)"
legend_constants[19] = "K_4 in component active_GAP (dimensionless)"
legend_states[3] = "GAPa in component active_GAP (dimensionless)"
legend_constants[20] = "K_5 in component RAS_to_GTP (dimensionless)"
legend_constants[21] = "K_6 in component RAS_to_GTP (dimensionless)"
legend_states[4] = "RGTP in component RAS_to_GTP (dimensionless)"
legend_constants[22] = "k_a in component adenylate_cyclase (per_micromolar_minute)"
legend_constants[23] = "k_i in component adenylate_cyclase (per_minute)"
legend_states[5] = "CYCLa in component adenylate_cyclase (dimensionless)"
legend_constants[24] = "K_7 in component active_PDE (dimensionless)"
legend_constants[25] = "K_8 in component active_PDE (dimensionless)"
legend_states[6] = "PDEa in component active_PDE (dimensionless)"
legend_constants[26] = "k_s in component cyclic_AMP (per_minute)"
legend_constants[27] = "k_d in component cyclic_AMP (per_minute)"
legend_constants[28] = "CYCLt in component cyclic_AMP (micromolar)"
legend_constants[29] = "K_md in component cyclic_AMP (micromolar)"
legend_constants[30] = "k_c9 in component V9 (per_minute)"
legend_constants[31] = "MSNt in component V9 (micromolar)"
legend_constants[51] = "V_9 in component V9 (per_minute)"
legend_constants[32] = "V_max10 in component V10 (micromolar_per_minute)"
legend_constants[52] = "V_10 in component V10 (per_minute)"
legend_constants[33] = "k_c11 in component V11 (per_minute)"
legend_constants[53] = "V_11 in component V11 (per_minute)"
legend_constants[34] = "V_max12 in component V12 (micromolar_per_minute)"
legend_constants[54] = "V_12 in component V12 (per_minute)"
legend_constants[35] = "k_t1 in component cytosol (per_minute)"
legend_constants[36] = "k_t2 in component cytosol (per_minute)"
legend_constants[37] = "K_11 in component cytosol (dimensionless)"
legend_constants[38] = "K_12 in component cytosol (dimensionless)"
legend_states[7] = "MN in component nucleus (dimensionless)"
legend_states[8] = "MCP in component cytosol_phos (dimensionless)"
legend_states[9] = "MC in component cytosol (dimensionless)"
legend_constants[39] = "K_9 in component nucleus (dimensionless)"
legend_constants[40] = "K_10 in component nucleus (dimensionless)"
legend_states[10] = "MNP in component nucleus_phos (dimensionless)"
legend_constants[41] = "k_t3 in component nucleus_phos (per_minute)"
legend_constants[42] = "k_t4 in component nucleus_phos (per_minute)"
legend_algebraic[1] = "M_cyto in component Mcyto (dimensionless)"
legend_algebraic[2] = "M_nucl in component Mnucl (dimensionless)"
legend_rates[2] = "d/dt GEFa in component active_GEF (dimensionless)"
legend_rates[3] = "d/dt GAPa in component active_GAP (dimensionless)"
legend_rates[4] = "d/dt RGTP in component RAS_to_GTP (dimensionless)"
legend_rates[5] = "d/dt CYCLa in component adenylate_cyclase (dimensionless)"
legend_rates[6] = "d/dt PDEa in component active_PDE (dimensionless)"
legend_rates[1] = "d/dt cAMP in component cyclic_AMP (micromolar)"
legend_rates[0] = "d/dt R2C2 in component holoenzyme_R_C (dimensionless)"
legend_rates[9] = "d/dt MC in component cytosol (dimensionless)"
legend_rates[7] = "d/dt MN in component nucleus (dimensionless)"
legend_rates[10] = "d/dt MNP in component nucleus_phos (dimensionless)"
legend_rates[8] = "d/dt MCP in component cytosol_phos (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 1
constants[1] = 4
constants[2] = 1
constants[3] = 1
constants[4] = 3.5
constants[5] = 0.3
constants[6] = 1.5
constants[7] = 1.3
constants[8] = 240
constants[9] = 250
constants[10] = 600
constants[11] = 3.333
constants[12] = 0.5
constants[13] = 1.5
constants[14] = 1
constants[15] = 1
states[0] = 0.5
states[1] = 1
constants[16] = 0.05
constants[17] = 0.05
states[2] = 0.36
constants[18] = 0.01
constants[19] = 0.01
states[3] = 0.5
constants[20] = 0.001
constants[21] = 0.001
states[4] = 0.1
constants[22] = 0.01
constants[23] = 1
states[5] = 0.1
constants[24] = 0.01
constants[25] = 0.01
states[6] = 0.5
constants[26] = 4
constants[27] = 100
constants[28] = 0.7
constants[29] = 20
constants[30] = 3.333
constants[31] = 1
constants[32] = 0.6
constants[33] = 3.333
constants[34] = 2
constants[35] = 10
constants[36] = 0.001
constants[37] = 0.05
constants[38] = 0.05
states[7] = 0.25
states[8] = 0.25
states[9] = 0.25
constants[39] = 0.05
constants[40] = 0.05
states[10] = 0.25
constants[41] = 0.001
constants[42] = 10
constants[43] = constants[0]/constants[1]
constants[44] = (constants[2]*constants[3])/constants[1]
constants[45] = (constants[4]*constants[5])/constants[6]
constants[46] = constants[7]/constants[6]
constants[47] = (constants[8]*constants[1])/constants[9]
constants[48] = (constants[10]*constants[6])/constants[9]
constants[49] = (constants[11]*constants[5])/constants[12]
constants[50] = constants[13]/constants[12]
constants[51] = (constants[30]*constants[5])/constants[31]
constants[52] = (constants[2]*constants[32])/constants[31]
constants[53] = (constants[33]*constants[5])/constants[31]
constants[54] = (constants[2]*constants[34])/constants[31]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[2] = (constants[43]*(1.00000-states[2]))/(constants[16]+(1.00000-states[2]))-(constants[44]*states[2])/(constants[17]+states[2])
rates[4] = (constants[47]*states[2]*(1.00000-states[4]))/(constants[20]+(1.00000-states[4]))-(constants[48]*states[3]*states[4])/(constants[21]+states[4])
rates[5] = constants[22]*states[4]*constants[9]*(1.00000-states[5])-constants[23]*states[5]
algebraic[3] = 2.00000*(1.00000-states[0])
rates[3] = (constants[45]*algebraic[3]*(1.00000-states[3]))/(constants[18]+(1.00000-states[3]))-(constants[46]*states[3])/(constants[19]+states[3])
rates[6] = (constants[49]*algebraic[3]*(1.00000-states[6]))/(constants[24]+(1.00000-states[6]))-(constants[50]*states[6])/(constants[25]+states[6])
algebraic[0] = 1.00000-states[0]
rates[0] = -constants[14]*states[0]*(power(states[1], 2.00000))+constants[15]*(power(algebraic[3], 2.00000))*algebraic[0]*(power(constants[5], 2.00000))*1.00000
rates[9] = ((-constants[35]*states[9]+constants[36]*states[7])-(constants[53]*algebraic[3]*states[9])/(constants[37]+states[9]))+(constants[54]*states[8])/(constants[38]+states[8])
rates[7] = ((constants[35]*states[9]-constants[36]*states[7])-(constants[51]*algebraic[3]*states[7])/(constants[39]+states[7]))+(constants[52]*states[10])/(constants[40]+states[10])
rates[10] = (((constants[51]*algebraic[3]*states[7])/(constants[39]+states[7])-(constants[52]*states[10])/(constants[40]+states[10]))+constants[41]*states[8])-constants[42]*states[10]
rates[8] = (-constants[41]*states[8]+constants[42]*states[10]+(constants[53]*algebraic[3]*states[9])/(constants[37]+states[9]))-(constants[54]*states[8])/(constants[38]+states[8])
algebraic[4] = constants[14]*states[0]*(power(states[1], 2.00000))-constants[15]*algebraic[3]*algebraic[0]*(power(constants[5], 2.00000))*1.00000
rates[1] = (constants[26]*states[5]*constants[28]-(constants[27]*constants[12]*states[6]*states[1])/(constants[29]+states[1]))-2.00000*algebraic[4]*constants[5]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = 2.00000*(1.00000-states[0])
algebraic[0] = 1.00000-states[0]
algebraic[4] = constants[14]*states[0]*(power(states[1], 2.00000))-constants[15]*algebraic[3]*algebraic[0]*(power(constants[5], 2.00000))*1.00000
algebraic[1] = states[9]+states[8]
algebraic[2] = states[7]+states[10]
return algebraic
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)